Question 169: Work, Energy and Power & Circular Motion

Question

A stone of mass ' m ' kg is tied to a string of length ' $L$ ' $m$ and moved in a vertical circle of radius 49 cm in a vertical plane. If it completes 30 revolutions per minute, the tension in the string when it is at the lowermost point is nearly [Take $\pi^2=10$ and acceleration due to gravity, $\mathrm{g}=10 \mathrm{~m} / \mathrm{s}^2$ ]

Accepted Answer

Tension in the string at the lowermost point is given by
$$ \begin{aligned} & T=m g+m \omega^2 r=m\left\{g+4 \pi^2 n^2 right\} \quad \ldots .[\omega=2 \pi n] \ & T=m\left[g+\left(4 \pi^2\left(\frac{n}{60}ight)^2 right)ight]=m\left[g+\left(\frac{\pi^2 n^2 r}{900}ight)ight] \ & T=m\left[10+\left(\frac{10 	imes 30^2 	imes 0.49}{900}ight)ight]=(15 m) N \end{aligned} $$

Answer

$(90 \mathrm{~m}) \mathrm{N}$

Answer

$\quad(60 \mathrm{~m}) \mathrm{N}$

Answer

$(45 m) \mathrm{N}$

Answer

$(15 m) \mathrm{N}$

Work, Energy and Power & Circular Motion

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